Results 21 to 30 of about 1,416,244 (110)

Some Borderenergetic and Equienergetic Graphs

Kragujevac Journal of Mathematics
The sum of absolute values of eigenvalues of a graph G is defined as energy of graph. If the energies of two non-isomorphic graphs are same then they are called equienergetic.
S. Vaidya, K. Popat
semanticscholar   +3 more sources

Distance Spectra of Some Double Join Operations of Graphs

International Journal of Mathematics and Mathematical Sciences
In literature, several types of join operations of two graphs based on subdivision graph, Q-graph, R-graph, and total graph have been introduced, and their spectral properties have been studied.
B. J. Manjunatha, B. R. Rakshith, K. N. Prakasha, N. V. Sayinath Udupa   +3 more
doaj   +2 more sources

Integral equienergetic non-isospectral unitary Cayley graphs

, 2020
We prove that the Cayley graphs $X(G,S)$ and $X^+(G,S)$ are equienergetic for any abelian group $G$ and any symmetric subset $S$. We then focus on the family of unitary Cayley graphs $G_R=X(R,R^*)$, where $R$ is a finite commutative ring with identity ...
Ricardo A. Podestá, Denis E. Videla
semanticscholar   +2 more sources

Seidel Equienergetic Graphs [PDF]

Bulletin of Mathematical Sciences and Applications, 2016
The Seidel matrix S(G) of a graph G is the square matrix with diagonal entries zeroes and off diagonal entries are - 1 or 1 corresponding to the adjacency and non-adjacency.
H. Ramane, Mahadevappa M. Gundloor, S. Hosamani   +2 more
semanticscholar   +2 more sources

New skew equienergetic oriented graphs [PDF]

Communications in Combinatorics and Optimization, 2019
Let $S(G^{\sigma})$ be the skew-adjacency matrix of the oriented graph $G^{\sigma}$, which is obtained from a simple undirected graph $G$ by assigning an orientation $\sigma$ to each of its edges.
X. Liu, L. Wang, C. Duan
doaj   +2 more sources

A graph operation and its applications in generating orderenergetic and equienergetic graphs [PDF]

MATCH Communications in Mathematical and in Computer Chemistry, 2021
A general graph operation is defined and some of its applications are given in this paper. The adjacency spectrum of any graph generated by this operation is given. A method for generating integral graphs using this operation is discussed.
S. Joseph
semanticscholar   +2 more sources

Several Methods for Generating Families of Orderenergetic, Integral and Equienergetic Graphs

match Communications in Mathematical and in Computer Chemistry, 2023
We define a general unary graph operation and give several applications of these operation in this paper. The adjacency matrix and the complete spectrum of the derived graphs are determined.
S. Joseph
semanticscholar   +3 more sources

Energy, Laplacian energy of double graphs and new families of equienergetic graphs [PDF]

AKCE International Journal of Graphs and Combinatorics, 2013
For a graph G with vertex set V(G) = {v1, v2, . . . , vn}, the extended double cover G* is a bipartite graph with bipartition (X, Y), X = {x1, x2, . . . , xn} and Y = {y1, y2, . . . , yn}, where two vertices xi and yj are adjacent if and only if i = j or
Hilal A. Ganie, S. Pirzada, A. Iványi
semanticscholar   +4 more sources

On irreducibility of eccentricity matrix of graphs and construction of $$\epsilon $$-equienergetic graphs [PDF]

Afrika Matematika
The eccentricity matrix $\epsilon(G)$, of a connected graph $G$ is obtained by retaining the maximum distance from each row and column of the distance matrix of $G$ and the other entries are assigned with 0. In this paper, we discuss the eccentricity spectrum of subdivision vertex (edge) join of regular graphs.
Anjitha Ashokan, Chithra A. V.
core   +4 more sources

Reciprocal complementary distance spectra and reciprocal complementary distance energy of line graphs of regular graphs [PDF]

Electronic Journal of Graph Theory and Applications, 2015
The reciprocal complementary distance (RCD) matrix of a graph $G$ is defined as $RCD(G) = [rc_{ij}]$ where $rc_{ij} = \frac{1}{1+D-d_{ij}}$ if $i \neq j$ and $rc_{ij} = 0$, otherwise, where $D$ is the diameter of $G$ and $d_{ij}$ is the distance between ...
Harishchandra S. Ramane, Ashwini S. Yalnaik   +1 more
doaj   +2 more sources